Calculating the covariance matrix of an object's points - Rotation of an object
I suggest using the addon Math vis to display vectors, in addition to testing your code in the console.

Paste the following in the console to see that the vertices are placed at the right locations. I don't know enough maths, but maybe the problem is in the numpy operations...

import bpy
import numpy

#from mathutils import Vector

from numpy import linalg as LA
vertices = bpy.context.active_object.data.vertices
matrix_world = bpy.context.active_object.matrix_world
verticesArray = numpy.zeros((3,len(vertices)))
counter = 0
for index, v in enumerate(vertices):
    globals()["vertex"+str(index)] = matrix_world * v.co ##vector to global variable
    world_coord = matrix_world * v.co
    verticesArray[0,counter]= world_coord[0]
    verticesArray[1,counter] = world_coord[1]
    verticesArray[2,counter] = world_coord[2]
    counter = counter + 1

convMat = numpy.cov(verticesArray)
eigenvalues, eigenvectors = LA.eig(convMat)
for index, vec in enumerate(eigenvectors):
    print(index, vec)
    globals()["vector"+str(index)] = Vector((vec[0], vec[1], vec[2]))

del world_coord
del matrix_world
print(eigenvectors)